For many years,the employment of the Wienr-Hopf technique to acoustics and other physical problems,was the only manifestation in applications of the Riemann-Hilbert formalism.However,in the last 50 years this formalism and its natural generalization called the d-bar formalism,have appeared in a large number of problems in mathematics and mathematical physics.In this lecture,I will review the impact of the above formalisms in the following:the development of a novel,hybrid numerical-analytics method for solving boundary value problems(Fokas Method,www.wikipedia.org/wiki/Fokas_method),the introduction of new algorithms in nuclear medical imaging,and most importantly,a novel approach to the Lindelof Hypothesis(a close relative of the Riemann Hypothesis).